I'd give up on this if I were you. Don't measure frequency change, make the oscillator a high impedance one and measure the LEVEL change.
I've used the first method and it's terribly unstable.
What you COULD do is pulse the coil and measure the Dv/Dt of the decay, OR just amplify and measure the level of the signal say 15uS after switch off, thus making a simple pulse induction metal detector. OR just Google "Geotech Forum" and take a look around there.
Good luck.